Question

Three circles touch each other each other externally. Find the radii of the circles if the sides of the triangle obtained by joining the centres are 10 cm, 14 cm and 16 cm respectively.

Answer 1

Let x be the radius of Circle A

Let y be the radius of Circle B

Let z be the radius of Circle C

$AB=x+y=10–eq.1$

$BC=y+z=14–eq.2$

$CA=z+x=16–eq.3$

From eq.3,

$z=16-x$

Substituting this in eq.2

$y+16–x=14$

$⟹y–x=1-eq.4$

Solving eq.1 and eq.4

$x=6$

$z=16-6=10$

$y=10-6=4$

Radii of circles are $6,10$ and $4$